This past week has seen growing confusion, indeed, chaos as the EU struggles to tackle the huge flow of migrants and asylum seekers that has continued even in the winter months. The spectre of compulsory quotas of asylum seekers has raised its head once again, albeit vigorously opposed by the East Europeans. Fortunately the UK has an opt-out on such quotas, but there have been threats that, if we exercise it, our current right to return applicants to the first EU country of arrival might be withdrawn.

To make matters even worse, a British court has ruled that the most recent EU directive requires us to consider asylum claims from close relatives of those who have applied for, or have been granted asylum in the UK – even if these relatives are still on mainland Europe. This is a recipe for a flood of claims and yet more applicants piling up in Calais to make their claims from there.

All this could hardly come at a more difficult time for the Prime Minister as he gears up voters for a referendum. He must hope that the French Prime Minister, Manuel Valls, is wrong to suggest that a deal cannot be concluded by February. A whole summer of headlines like those of this week might well make it extremely difficult for the Prime Minister to win the referendum. We take different views on Europe but we both currently expect that to be the likely outcome.

Public concern will only intensify if voters focus on official population projections for the UK. Our population is set to grow by nearly 10 million people in the next 25 years – to over 74 million. About two-thirds of this increase will be due to future immigrants and their children. The tale doesn’t end there, though.

This official projection assumes that net migration will average only about 185,000 a year over that period; a little over half the current rate of 330,000. There is an official “high migration” assumption that envisages net migration at 265,000 a year and notes that if this occurs our population will increase by 16 million over the next 25 years. That’s 16 more Birminghams. No one believes that anything like the equivalent increase in house building, roads or schools is on the cards. The result is bound to be a decline in living standards.

Casting their eyes over the official projections, voters are likely to conclude that current levels of immigration, with many new arrivals coming from Eastern Europe, are completely unsustainable. Indeed, 70 per cent of the public already wish to see a reduction in immigration. To continue with an open-door policy therefore goes against the grain of voters’ wishes, and carries the risk that social cohesion could also suffer. Our country already has changed beyond recognition over the past decade.

Almost on a daily basis we are confronted with the problems of having no firm borders with Europe, and of Europe itself having no firm borders with the rest of the world. Germany too is undergoing rapid change, having added a million people to its population in around six months.

It is therefore vital for the Prime Minister to achieve an agreement with other European leaders that offers a fighting chance of being able to control the mass movement of people. Given that public budgets will continue to be screwed down, an unprecedented population increase will clearly have massive consequences for our public services and infrastructure. For all the key services – housing, schools and health – voters know how tough it will be to meet the needs of the existing population, let alone the 10 million (or 16 million or more) newcomers of the next 25 years.

The need for housing is now really urgent. It is estimated that the UK needs to build 240,000 homes a year – nearly one every two minutes. Between 2000 and 2014 two-thirds of the additional households created in the UK were headed by a person who was born abroad. While the recent announcement of 13,000 new homes on public land is to be welcomed, it is a drop in the ocean compared with the huge scale of the population increase now confronting us.

Any serious attempt to solve the housing shortage must include redoubling efforts to bring net migration back to the levels of the 1990s – tens of thousands – and an even larger house building programme to meet the needs of those families already waiting for far too long in the housing queue.

Moreover, each year, a large and growing number of parents find they cannot get their children into their chosen school. In London, where the shortage of places can be particularly acute, two-thirds of births are now to parents where one or both was born overseas.

As for the health service, the NHS patient base will have risen in the decade come 2020 by 4.5 million – a giant 7 per cent increase in the number of people using a service while its real budget, allowing for inflation, is falling. This is likely to bring about, sooner rather than later, a financial implosion within the NHS.

We both hope that the Prime Minister will return with a genuine and effective deal on immigration, lest he finds that his case to remain in the EU has been seriously undermined.

Sir Nicholas Soames MP and Frank Field MP are co-chairmen of the cross-party group on balanced migration